Related papers: Characterizing Multivariate Information Flows
Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible $N$--point correlation is measured by a decrease…
Information theory is an outstanding framework to measure uncertainty, dependence and relevance in data and systems. It has several desirable properties for real world applications: it naturally deals with multivariate data, it can handle…
We propose a new estimator to measure directed dependencies in time series. The dimensionality of data is first reduced using a new non-uniform embedding technique, where the variables are ranked according to a weighted sum of the amount of…
The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…
Identifying the origin of nonequilibrium characteristics in a generic interacting system having multiple degrees of freedom is a challenging task. In this context, information theoretic measures such as mutual information and related…
The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…
Measures of dependence among variables, and measures of information content and shared information have become valuable tools of multi-variable data analysis. Information measures, like marginal entropies, mutual and multi-information, have…
Multi-layered networks represent a major advance in the description of natural complex systems, and their study has shed light on new physical phenomena. Despite its importance, however, the role of the temporal dimension in their structure…
Transient phenomena play a key role in coordinating brain activity at multiple scales, however,their underlying mechanisms remain largely unknown. A key challenge for neural data science is thus to characterize the network interactions at…
Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative…
Information-theoretic quantities, such as entropy, are used to quantify the amount of information a given variable provides. Entropies can be used together to compute the mutual information, which quantifies the amount of information two…
Pairwise interactions between individuals are taken as fundamental drivers of collective behavior responsible for group cohesion and decision-making. While an individual directly influences only a few neighbors, over time indirect…
The interactions between three or more random variables are often nontrivial, poorly understood, and yet, are paramount for future advances in fields such as network information theory, neuroscience, genetics and many others. In this work,…
Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is…
The fundamental building block of social influence is for one person to elicit a response in another. Researchers measuring a "response" in social media typically depend either on detailed models of human behavior or on platform-specific…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…
We propose a novel tensor-based formalism for inferring causal structures from time series. An information theoretical analysis of transfer entropy, shows that transfer entropy results from transmission of information over a set of…
We introduce an epistemic information measure between two data streams, that we term $influence$. Closely related to transfer entropy, the measure must be estimated by epistemic agents with finite memory resources via sampling accessible…
Inferring causal relationships from observed data is an important task, yet it becomes challenging when the data is subject to various external interferences. Most of these interferences are the additional effects of external factors on…
The concepts of information transfer and causal effect have received much recent attention, yet often the two are not appropriately distinguished and certain measures have been suggested to be suitable for both. We discuss two existing…